Does charging your phone in the car affect the battery?

If you're asking about the car battery, the practical answer is "No."; the drain on the car battery would be negligible. The current used would be significantly less than 1 of your interior dome lights while the phone is charging, and once the phone is fully charged it (and the charger) would consume even less.

If you're asking about the phone's battery, the only effect would be a charged battery. The process does not promote an unhealthy state for either battery in any practical or realistic scenario.